Finite Group Databasebeta

← #7712770

Subgroups — #7712770

Order 512.

5212 conjugacy classes of subgroups.

The subgroup lattice has 1317 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59228C212yesmaximal, complemented
2#59212C212yesmaximal, complemented
3#59050C212yesmaximal, complemented
4#59034C212yesmaximal, complemented
5#45515C214yesmaximal, complemented
6#45514C214yesmaximal, complemented
7#39783C214yesmaximal, complemented
8#39781C214yesmaximal, complemented
9#39515C212yesmaximal, complemented
10#39507C212yesmaximal, complemented
11#39498C212yesmaximal, complemented
12#39491C212yesmaximal, complemented
13#39196C214yesmaximal, complemented
14#39194C212yesmaximal, complemented
15#39193C212yesmaximal, complemented
16#37621C212yesmaximal, complemented
17#37325C214yesmaximal, complemented
18#36645C211yesmaximal, characteristic, complemented
19#36631C211yesmaximal, characteristic, complemented
20#36210C212yesmaximal, complemented
21#36194C211yesmaximal, characteristic, complemented
22#36187C211yesmaximal, characteristic, complemented
23#36150C212yesmaximal, complemented
24#36134C211yesmaximal, characteristic, complemented
25#36127C211yesmaximal, characteristic, complemented
26#35297C212yesmaximal, complemented
27#35292C212yesmaximal, complemented
28#34383C212yesmaximal, complemented
29C4×#532C211yesmaximal, characteristic, complemented
30C2×#555C2212yes—
31C2×#547C2212yes—
32C2×#533C2212yes—
33C2×#533C2212yes—
34C2×#532C2211yescharacteristic
35C2×#532C2212yes—
36C2×#529C2212yes—
37C2×C4×#41C2212yes—
38#2868C2211yescharacteristic
39#2868C2211yescharacteristic
40#2862C2212yes—
41#2861C2212yes—
42#2860C2212yes—
43#2860C2212yes—
44#2859C2211yescharacteristic
45#2859C2212yes—
46#2859C2212yes—
47#2858C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2857C2212yes—
53#2857C2212yes—
54#2857C2212yes—
55#2857C2212yes—
56#2856C2211yescharacteristic
57#2856C2212yes—
58#2854C2212yes—
59#2854C2212yes—
60#2850C2212yes—
61#2813C2218yes—
62#2807C2218yes—
63#2803C2218yes—
64#2803C2218yes—
65#2801C2218yes—
66#2800C2218yes—
67#2798C2218yes—
68#2788C2218yes—
69#2779C2218yes—
70#2778C2218yes—
71#2759C2218yes—
72#2757C2218yes—
73#2756C2218yes—
74#2730C2218yes—
75#2710C2218yes—
76#2710C2218yes—
77#2696C2218yes—
78#2662C2218yes—
79#2628C2214yes—
80#2625C2214yes—
81#2624C2214yes—
82#2619C2214yes—
83#2616C2214yes—
84#2615C2214yes—
85#2595C2218yes—
86#2593C2218yes—
87#2592C2214yes—
88#2584C2214yes—
89#2581C2214yes—
90#2580C2214yes—
91#2571C2212yes—
92#2563C2212yes—
93#2563C2212yes—
94#2562C2214yes—
95#2562C2214yes—
96#2552C2212yes—
97#2547C2212yes—
98#2542C2212yes—
99#2540C2214yes—
100#2540C2214yes—
101#2538C2212yes—
102#2538C2212yes—
103#2537C2212yes—
104#2537C2212yes—
105#2537C2212yes—
106#2537C2212yes—
107#2536C2214yes—
108#2535C2214yes—
109#2514C2214yes—
110#2509C2214yes—
111#2504C2214yes—
112#2500C2214yes—
113#2500C2214yes—
114#2497C2214yes—
115#2495C2214yes—
116#2495C2214yes—
117#2494C2214yes—
118#2494C2214yes—
119#2494C2214yes—
120#2492C2214yes—
121#2491C2214yes—
122#2491C2214yes—
123#2490C2214yes—
124#2490C2214yes—
125#2490C2214yes—
126#2485C2214yes—
127#2485C2214yes—
128#2485C2214yes—
129#2458C2218yes—
130#2454C2214yes—
131#2448C2218yes—
132#2448C2214yes—
133#2442C2214yes—
134#2441C2214yes—
135#2441C2214yes—
136#2439C2214yes—
137#2432C2214yes—
138#2429C2214yes—
139#2427C2214yes—
140#2426C2214yes—
141#2426C2214yes—
142#2423C2214yes—
143#2422C2214yes—
144#2422C2214yes—
145#2421C2214yes—
146#2415C2214yes—
147#2415C2214yes—
148#2415C2214yes—
149#2414C2214yes—
150#2414C2214yes—
151#2414C2214yes—
152#2414C2214yes—
153#2414C2214yes—
154#2407C2214yes—
155#2407C2214yes—
156#2407C2214yes—
157#2376C2218yes—
158#2370C2214yes—
159#2369C2212yes—
160#2367C2214yes—
161#2365C2212yes—
162#2363C2214yes—
163#2362C2214yes—
164#2355C2212yes—
165#2354C2212yes—
166#2354C2212yes—
167#2354C2212yes—
168#2354C2214yes—
169#2354C2212yes—
170#2352C2214yes—
171Q8×C4⋊C4C2212yes—
172D4×C4⋊C4C2212yes—
173D4×C4⋊C4C2212yes—
174#2347C2214yes—
175#2341C2214yes—
176#2334C2218yes—
177#2324C2214yes—
178#2324C2214yes—
179#2323C2214yes—
180#2323C2214yes—
181#2317C2214yes—
182#2314C2214yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2212yes—
185C4×C4⋊Q8C2212yes—
186C4×C4⋊Q8C2212yes—
187C4×C4⋊Q8C2212yes—
188C4×C4⋊Q8C2211yescharacteristic
189C4×C4⋊Q8C2211yescharacteristic
190C4×#127C2211yescharacteristic
191C4×#127C2211yescharacteristic
192C4×#127C2211yescharacteristic
193C4×#124C2212yes—
194C4×#124C2212yes—
195C4×#124C2212yes—
196C4×#121C2212yes—
197C4×#121C2212yes—
198C4×#121C2211yescharacteristic
199C4×#121C2211yescharacteristic
200C4×#121C2211yescharacteristic
201C4×#121C2211yescharacteristic
202C4×#121C2212yes—
203C4×#121C2212yes—
204#2297C2212yes—
205#2293C2212yes—
206#2293C2212yes—
207#2293C2211yescharacteristic
208#2293C2211yescharacteristic
209#2293C2212yes—
210#2285C2212yes—
211#2285C2212yes—
212#2285C2211yescharacteristic
213#2285C2212yes—
214#2285C2212yes—
215C42×D4C2211yescharacteristic
216C42×D4C2211yescharacteristic
217C42×D4C2212yes—
218C2×C43C2211yescharacteristic
219C22×#41C2312yes—
220C22×#41C2314yes—
221#555—48no—
222#547—48no—
223#533—48no—
224#533—48no—
225#532—28no—
226#532—48no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2312yes—
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2312yes—
235C2×#127C2311yescharacteristic
236C2×#127C2311yescharacteristic
237#529—216no—
238C2×#126C2314yes—
239C2×#125C2312yes—
240C2×#125C2314yes—
241C2×#125C2314yes—
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2314yes—
245C2×#124C2312yes—
246C2×#124C2318yes—
247C2×#123C2314yes—
248C2×#123C2318yes—
249C2×C22⋊Q8C2312yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×#121C2312yes—
258C2×#121C2311yescharacteristic
259C2×#121C2311yescharacteristic
260C2×#121C2312yes—
261C2×#121C2314yes—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2314yes—
265C2×#121C2314yes—
266C2×#121C2314yes—
267C2×#121C2314yes—
268C2×#121C2314yes—
269C2×#121C2314yes—
270C4×#41—48no—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2314yes—
273C2×C4×Q8C2314yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2314yes—
277C2×C4×Q8C2314yes—
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2311yescharacteristic
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2312yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2314yes—
295C2×C4×D4C2314yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×#117C2314yes—
300C2×#117C2314yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2314yes—
305C2×#117C2314yes—
306C2×#117C2314yes—
307C2×#117C2314yes—
308C22×C4⋊C4C2314yes—
309C22×C42C2311yescharacteristic
310C22×C42C2312yes—
311C22×C42C2312yes—
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318#401C2318yes—
319#400C2318yes—
320#400C2318yes—
321#400C2318yes—
322#400C2318yes—
323#399C2318yes—
324#399C2318yes—
325#399C2318yes—
326#398C2318yes—
327#398C2318yes—
328#397C2318yes—
329#397C2318yes—
330#397C2318yes—
331#397C2318yes—
332#397C2318yes—
333#397C2318yes—
334#397C2318yes—
335#396C2318yes—
336#396C2318yes—
337#396C2318yes—
338#395C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2318yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2318yes—
351#393C2318yes—
352#393C2318yes—
353#393C2318yes—
354#392C2318yes—
355#392C2318yes—
356#392C2318yes—
357#392C2318yes—
358#391C2314yes—
359#391C2312yes—
360#391C2314yes—
361#391C2314yes—
362#391C2314yes—
363#391C2312yes—
364#391C2312yes—
365#391C2312yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2318yes—
370#390C2312yes—
371#390C2312yes—
372#390C2312yes—
373#390C2312yes—
374#390C2312yes—
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2312yes—
380#390C2312yes—
381#390C2314yes—
382#390C2314yes—
383#390C2312yes—
384#390C2314yes—
385#390C2318yes—
386#390C2318yes—
387#390C2312yes—
388#390C2314yes—
389#390C2312yes—
390#390C2318yes—
391#390C2318yes—
392#390C2312yes—
393#390C2318yes—
394#390C2312yes—
395#390C2312yes—
396#390C2312yes—
397#390C2314yes—
398#389C2314yes—
399#389C2314yes—
400#389C2312yes—
401#389C2312yes—
402#389C2314yes—
403#389C2314yes—
404#389C2314yes—
405#389C2314yes—
406#389C2314yes—
407#389C2314yes—
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2312yes—
413#389C2312yes—
414#389C2314yes—
415#389C2314yes—
416#389C2318yes—
417#389C2318yes—
418#389C2318yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2312yes—
423#389C2314yes—
424#389C2312yes—
425#389C2314yes—
426#389C2318yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2314yes—
432#388C2318yes—
433#388C2318yes—
434#388C2318yes—
435#388C2318yes—
436#388C2318yes—
437#388C2318yes—
438#388C2318yes—
439#388C2318yes—
440#388C2318yes—
441#388C2318yes—
442#388C2318yes—
443#388C2312yes—
444#388C2314yes—
445#388C2318yes—
446#388C2318yes—
447#388C2314yes—
448#388C2314yes—
449#388C2312yes—
450#388C2318yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2318yes—
456#388C2314yes—
457#388C2318yes—
458#388C2318yes—
459#388C2312yes—
460#388C2312yes—
461#388C2312yes—
462#388C2312yes—
463#388C2312yes—
464#388C2312yes—
465#387C2318yes—
466#387C2318yes—
467#387C2318yes—
468#387C2318yes—
469#387C2318yes—
470#387C2318yes—
471#387C2318yes—
472#386C2318yes—
473#386C2318yes—
474#386C2314yes—
475#386C2314yes—
476#386C2318yes—
477#386C2312yes—
478#386C2312yes—
479#386C2312yes—
480#386C2312yes—
481#385C2318yes—
482#385C2318yes—
483#385C2318yes—
484#385C2318yes—
485#385C2318yes—
486#384C2311yescharacteristic
487#384C2311yescharacteristic
488#384C2311yescharacteristic
489#384C2311yescharacteristic
490#384C2312yes—
491#384C2312yes—
492#384C2312yes—
493#384C2312yes—
494#384C2312yes—
495#384C2314yes—
496#384C2312yes—
497#384C2312yes—
498#384C2312yes—
499#383C2318yes—
500#382C2314yes—
501#382C2314yes—
502#382C2314yes—
503#382C2314yes—
504#382C2312yes—
505#382C2312yes—
506#382C2314yes—
507#380C2312yes—
508#380C2314yes—
509#380C2314yes—
510#380C2314yes—
511#380C2314yes—
512#380C2314yes—
513#380C2314yes—
514#380C2314yes—
515#380C2314yes—
516#380C2314yes—
517#380C2314yes—
518#380C2314yes—
519#380C2314yes—
520#380C2314yes—
521#380C2318yes—
522#380C2312yes—
523#380C2314yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2311yescharacteristic
528#380C2311yescharacteristic
529#380C2312yes—
530#380C2314yes—
531C4×C4⋊C4C2314yes—
532C4×C4⋊C4C2314yes—
533C4×C4⋊C4C2314yes—
534C4×C4⋊C4C2314yes—
535C4×C4⋊C4C2314yes—
536C4×C4⋊C4C2311yescharacteristic
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2311yescharacteristic
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2311yescharacteristic
541C4×C4⋊C4C2311yescharacteristic
542C4×C4⋊C4C2312yes—
543C4×C4⋊C4C2312yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2314yes—
546C4×C4⋊C4C2314yes—
547C4×C4⋊C4C2314yes—
548C4×C4⋊C4C2318yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2311yescharacteristic
551C4×C4⋊C4C2311yescharacteristic
552C4×C4⋊C4C2312yes—
553C4×C22⋊C4C2318yes—
554C4×C22⋊C4C2312yes—
555C4×C22⋊C4C2312yes—
556C4×C22⋊C4C2312yes—
557C4×C22⋊C4C2312yes—
558C4×C22⋊C4C2312yes—
559C4×C22⋊C4C2312yes—
560C4×C22⋊C4C2312yes—
561C4×C22⋊C4C2312yes—
562C4×C22⋊C4C2312yes—
563C4×C22⋊C4C2312yes—
564C4×C22⋊C4C2312yes—
565C4×C22⋊C4C2312yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C43C2311yescharacteristic
569C43C2311yescharacteristic
570C43C2311yescharacteristic
571C43C2311yescharacteristic
572C43C2311yescharacteristic
573C43C2311yescharacteristic
574C43C2311yescharacteristic
575C43C2311yescharacteristic
576C2×#41—28no—
577C2×#41—44no—
578C2×#41—44no—
579C2×#41—48no—
580C2×#41—48no—
581C2×#41—48no—
582C22×Q8C2412yes—
583C22×Q8C2414yes—
584C22×Q8C2412yes—
585C22×Q8C2414yes—
586C22×D4C2412yes—
587C22×D4C2411yescharacteristic
588C22×D4C2411yescharacteristic
589C22×D4C2412yes—
590C22×D4C2412yes—
591C22×D4C2412yes—
592C22×D4C2412yes—
593C22×D4C2412yes—
594C22×D4C2412yes—
595C22×D4C2414yes—
596C22×D4C2418yes—
597C22×D4C2418yes—
598C23×C4C2414yes—
599C23×C4C2412yes—
600C23×C4C2412yes—
601C23×C4C2412yes—
602C23×C4C2412yes—
603C23×C4C2412yes—
604C23×C4C2411yescharacteristic
605C23×C4C2411yescharacteristic
606C23×C4C2412yes—
607C23×C4C2411yescharacteristic
608C23×C4C2411yescharacteristic
609C23×C4C2411yescharacteristic
610C23×C4C2411yescharacteristic
611C23×C4C2418yes—
612C23×C4C2411yescharacteristic
613C4⋊Q8—24no—
614C4⋊Q8—28no—
615C4⋊Q8—24no—
616C4⋊Q8—28no—
617C4⋊Q8—28no—
618C4⋊Q8—44no—
619C4⋊Q8—44no—
620C4⋊Q8—44no—
621#127—24no—
622#127—24no—
623#126—216no—
624#125—28no—
625#125—48no—
626#125—48no—
627#124—28no—
628#124—28no—
629#124—44no—
630#124—48no—
631#124—416no—
632#123—216no—
633#123—416no—
634C22⋊Q8—28no—
635C22⋊Q8—48no—
636C22⋊Q8—48no—
637C22⋊Q8—48no—
638C22⋊Q8—48no—
639C22⋊Q8—48no—
640C22⋊Q8—48no—
641C22⋊Q8—48no—
642#121—28no—
643#121—24no—
644#121—24no—
645#121—28no—
646#121—44no—
647#121—48no—
648#121—44no—
649#121—48no—
650#121—48no—
651#121—48no—
652#121—48no—
653#121—48no—
654#121—48no—
655C4×Q8—28no—
656C4×Q8—44no—
657C4×Q8—44no—
658C4×Q8—48no—
659C4×Q8—48no—
660C4×Q8—48no—
661C4×Q8—48no—
662C4×D4—216no—
663C4×D4—28no—
664C4×D4—24no—
665C4×D4—24no—
666C4×D4—28no—
667C4×D4—24no—
668C4×D4—28no—
669C4×D4—24no—
670C4×D4—28no—
671C4×D4—24no—
672C4×D4—24no—
673C4×D4—48no—
674C4×D4—48no—
675C4×D4—44no—
676C4×D4—44no—
677C4×D4—44no—
678C4×D4—44no—
679C4×D4—44no—
680C4×D4—44no—
681C4×D4—44no—
682C4×D4—44no—
683#117—216no—
684#117—44no—
685#117—44no—
686#117—44no—
687#117—48no—
688#117—48no—
689#117—48no—
690#117—48no—
691#117—48no—
692C2×C4⋊C4—48no—
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2411yescharacteristic
696C2×C4⋊C4C2412yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2412yes—
699C2×C4⋊C4C2412yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2412yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2412yes—
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2418yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2418yes—
730C2×C4⋊C4C2418yes—
731C2×C4⋊C4C2418yes—
732C2×C4⋊C4C2418yes—
733C2×C4⋊C4C2418yes—
734C2×C4⋊C4C2418yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2412yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2412yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2412yes—
752C2×C22⋊C4C2412yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2412yes—
755C2×C22⋊C4C2412yes—
756C2×C22⋊C4C2412yes—
757C2×C22⋊C4C2412yes—
758C2×C22⋊C4C2412yes—
759C2×C22⋊C4C2412yes—
760C2×C22⋊C4C2418yes—
761C2×C22⋊C4C2418yes—
762C2×C22⋊C4C2418yes—
763C2×C22⋊C4C2418yes—
764C2×C22⋊C4C2418yes—
765C2×C22⋊C4C2418yes—
766C2×C22⋊C4C2418yes—
767C2×C22⋊C4C2412yes—
768C2×C22⋊C4C2412yes—
769C2×C22⋊C4C2412yes—
770C2×C22⋊C4C2412yes—
771C2×C22⋊C4C2418yes—
772C2×C22⋊C4C2418yes—
773C2×C22⋊C4C2414yes—
774C2×C22⋊C4C2414yes—
775C2×C22⋊C4C2418yes—
776C2×C22⋊C4C2418yes—
777C2×C22⋊C4C2418yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C42—24no—
781C2×C42—28no—
782C2×C42—28no—
783C2×C42—24no—
784C2×C42—24no—
785C2×C42—42no—
786C2×C42—42no—
787C2×C42—42no—
788C2×C42#4118yescomplemented
789C2×C42C2411yescharacteristic
790C2×C42C2412yes—
791C2×C42C2412yes—
792C2×C42C2414yes—
793C2×C42C2412yes—
794C2×C42C2411yescharacteristic
795C2×C42C2411yescharacteristic
796C2×C42C2411yescharacteristic
797C2×C42C2411yescharacteristic
798C2×C42C2412yes—
799C2×C42C2412yes—
800C2×C42C2412yes—
801C2×C42C2411yescharacteristic
802C2×C42C2411yescharacteristic
803C2×C42C2411yescharacteristic
804C2×C42C2411yescharacteristic
805C2×C42C2411yescharacteristic
806C2×C42C2411yescharacteristic
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2411yescharacteristic
810C2×C42C2411yescharacteristic
811C2×C42C2418yes—
812C2×C42C2418yes—
813C2×C42C2418yes—
814C2×C42C2418yes—
815C2×C42C2411yescharacteristic
816C2×C42C2411yescharacteristic
817C2×C42C2411yescharacteristic
818C2×C42C2411yescharacteristic
819C2×C42C2411yescharacteristic
820C2×C42C2411yescharacteristic
821C2×C42C2411yescharacteristic
822C2×C42C2411yescharacteristic
823C2×C42C2411yescharacteristic
824C2×C42C2411yescharacteristic
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2411yescharacteristic
828#95C2412yes—
829#95C2412yes—
830#95C2412yes—
831#95C2412yes—
832#95C2412yes—
833#95C2412yes—
834#95C2412yes—
835#95C2412yes—
836#95C2412yes—
837#95C2412yes—
838#95C2412yes—
839#95C2412yes—
840#95C2418yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2418yes—
846#95C2418yes—
847#95C2418yes—
848#95C2418yes—
849#95C2418yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2414yes—
857#95C2414yes—
858#95C2418yes—
859#95C2418yes—
860C24C2514yes—
861C24C2512yes—
862C24C2512yes—
863C24C2511yescharacteristic
864#41—432no—
865#41—832no—
866C2×Q8—24no—
867C2×Q8—24no—
868C2×Q8—24no—
869C2×Q8—28no—
870C2×Q8—28no—
871C2×Q8—28no—
872C2×Q8—24no—
873C2×Q8—28no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—44no—
877C2×Q8—44no—
878C2×D4—24no—
879C2×D4—24no—
880C2×D4—28no—
881C2×D4—24no—
882C2×D4—24no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—24no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—24no—
889C2×D4—24no—
890C2×D4—24no—
891C2×D4—24no—
892C2×D4—22no—
893C2×D4—22no—
894C2×D4—24no—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—48no—
907C2×D4—48no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—48no—
911C2×D4—48no—
912C2×D4—48no—
913C2×D4—48no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—28no—
919C22×C4—24no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—24no—
927C22×C4—24no—
928C22×C4—24no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—28no—
932C22×C4—24no—
933C22×C4—24no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—28no—
937C22×C4—24no—
938C22×C4—24no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—24no—
945C22×C4—24no—
946C22×C4—24no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—41no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—48no—
954C22×C4—48no—
955C22×C4—48no—
956C22×C4C2×#4114yes—
957C22×C4C2×#4114yes—
958C22×C4C2×#4114yes—
959C22×C4C2511yescharacteristic
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2511yescharacteristic
963C22×C4C2514yes—
964C22×C4C2514yes—
965C22×C4C2512yes—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2518yes—
969C22×C4C2511yescharacteristic
970C22×C4C2514yes—
971C22×C4C2518yes—
972C22×C4C2511yescharacteristic
973C22×C4C2512yes—
974C22×C4C2511yescharacteristic
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C22×C4C2511yescharacteristic
978C22×C4C2511yescharacteristic
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C4⋊C4—28no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—28no—
993C4⋊C4—22no—
994C4⋊C4—28no—
995C4⋊C4—22no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—24no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—24no—
1003C4⋊C4—28no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—28no—
1009C4⋊C4—24no—
1010C4⋊C4—28no—
1011C4⋊C4—48no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—48no—
1021C4⋊C4—48no—
1022C4⋊C4—48no—
1023C4⋊C4—48no—
1024C4⋊C4—48no—
1025C4⋊C4—48no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C22⋊C4—28no—
1031C22⋊C4—28no—
1032C22⋊C4—28no—
1033C22⋊C4—24no—
1034C22⋊C4—24no—
1035C22⋊C4—24no—
1036C22⋊C4—24no—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—24no—
1040C22⋊C4—28no—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—24no—
1044C22⋊C4—28no—
1045C22⋊C4—48no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C22⋊C4—48no—
1055C22⋊C4—48no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—48no—
1061C22⋊C4—48no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—48no—
1065C22⋊C4—48no—
1066C22⋊C4—48no—
1067C22⋊C4—48no—
1068C22⋊C4—48no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C42—28no—
1072C42—22no—
1073C42—24no—
1074C42—24no—
1075C42—24no—
1076C42—22no—
1077C42—22no—
1078C42—24no—
1079C42—24no—
1080C42—24no—
1081C42—22no—
1082C42—22no—
1083C42—22no—
1084C42—22no—
1085C42—22no—
1086C42—22no—
1087C42—22no—
1088C42—22no—
1089C42—22no—
1090C42—22no—
1091C42—22no—
1092C42—22no—
1093C42—41no—
1094C42—41no—
1095C42—41no—
1096C42—41no—
1097C42—41no—
1098C42—41no—
1099C42—48no—
1100C42—48no—
1101C42—48no—
1102C42—48no—
1103C42C2×#4114yes—
1104C42C2×#4114yes—
1105C42C2×#4114yes—
1106C42C2×#4114yes—
1107C42H(5,𝔽2)14yes—
1108C42H(5,𝔽2)14yes—
1109C422−1+414yes—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—24no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—24no—
1122C23—22no—
1123C23—24no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—24no—
1128C23—22no—
1129C23—22no—
1130C23—22no—
1131C23—24no—
1132C23—24no—
1133C23—22no—
1134C23—22no—
1135C23—24no—
1136C23—22no—
1137C23C22×#4112yes—
1138C23C2611yescharacteristic
1139Q8—48no—
1140Q8—48no—
1141Q8—416no—
1142Q8—88no—
1143D4—48no—
1144D4—48no—
1145D4—48no—
1146D4—48no—
1147D4—48no—
1148D4—44no—
1149D4—44no—
1150D4—48no—
1151D4—48no—
1152D4—88no—
1153D4—816no—
1154D4—168no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—28no—
1168C2×C4—28no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—24no—
1186C2×C4—28no—
1187C2×C4—24no—
1188C2×C4—28no—
1189C2×C4—28no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—24no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—24no—
1204C2×C4—28no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—28no—
1210C2×C4—22no—
1211C2×C4—28no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—44no—
1215C2×C4—44no—
1216C2×C4—44no—
1217C2×C4—48no—
1218C2×C4—48no—
1219C2×C4—416no—
1220C2×C4—44no—
1221C2×C4—48no—
1222C2×C4—48no—
1223C2×C4—44no—
1224C2×C4—48no—
1225C2×C4—48no—
1226C2×C4—816no—
1227C2×C4C22×#4112yes—
1228C2×C4C22×#4112yes—
1229C2×C4C22×#4112yes—
1230C2×C4C22×#4112yes—
1231C2×C4C22×#4112yes—
1232C2×C4C22×#4112yes—
1233C2×C4C2×H(5,𝔽2)12yes—
1234C2×C4C2×H(5,𝔽2)12yes—
1235C2×C4C2×H(5,𝔽2)12yes—
1236C2×C4C2×H(5,𝔽2)12yes—
1237C2×C4C2×H(5,𝔽2)12yes—
1238C2×C4C2×H(5,𝔽2)12yes—
1239C2×C4C2×2−1+412yes—
1240C2×C4C2×2−1+412yes—
1241C2×C4C2×2−1+412yes—
1242C2×C4#58512yes—
1243C2×C4#58512yes—
1244C2×C4#58512yes—
1245C22—22no—
1246C22—22no—
1247C22—22no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—42no—
1253C22—42no—
1254C22—44no—
1255C22—42no—
1256C22—42no—
1257C22—44no—
1258C22—42no—
1259C22—42no—
1260C22—44no—
1261C22—44no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—44no—
1267C22—42no—
1268C22—44no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—44no—
1273C22C23×#4111yescharacteristic
1274C22C22×H(5,𝔽2)11yescharacteristic
1275C22C22×H(5,𝔽2)11yescharacteristic
1276C22C22×2−1+411yescharacteristic
1277C22C2×#58511yescharacteristic
1278C22C2×#58511yescharacteristic
1279C22C2×#58511yescharacteristic
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—22no—
1285C4—22no—
1286C4—41no—
1287C4—42no—
1288C4—42no—
1289C4—48no—
1290C4—42no—
1291C4—42no—
1292C4—41no—
1293C4—42no—
1294C4—42no—
1295C4—44no—
1296C4—44no—
1297C4—44no—
1298C4—41no—
1299C4—48no—
1300C4—41no—
1301C4#350614yes—
1302C4#351114yes—
1303C4#354614yes—
1304C4#354714yes—
1305C2—42no—
1306C2—82no—
1307C2—82no—
1308C2—84no—
1309C2C2×#354611yescharacteristic
1310C2C2×#354711yescharacteristic
1311C2C2×#350611yescharacteristic
1312C2C2×#351111yescharacteristic
1313C2#6281511yescharacteristic
1314C2#6283611yescharacteristic
1315C2#6283811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59228C2semidirect
2. #59212C2semidirect
3. #59050C2semidirect
4. #59034C2semidirect
5. #45515C2semidirect
6. #45514C2semidirect
7. #39783C2semidirect
8. #39781C2semidirect
9. #39515C2semidirect
10. #39507C2semidirect
11. #39498C2semidirect
12. #39491C2semidirect
13. #39196C2semidirect
14. #39194C2semidirect
15. #39193C2semidirect
16. #37621C2semidirect
17. #37325C2semidirect
18. #36645C2semidirect
19. #36631C2semidirect
20. #36210C2semidirect
21. #36194C2semidirect
22. #36187C2semidirect
23. #36150C2semidirect
24. #36134C2semidirect
25. #36127C2semidirect
26. #35297C2semidirect
27. #35292C2semidirect
28. #34383C2semidirect
29. C4×#532C2semidirect
788. C2×C42#41semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#592282
#592122
#590502
#590342
#455152
#455142
#397832
#397812
#395152
#395072
#394982
#394912
#391962
#391942
#391932
#376212
#373252
#366452
#366312
#362102
#361942
#361872
#361502
#361342
#361272
#352972
#352922
#343832
C4×#5322